Algebra 2 Lesson #80 Solving Non-Linear Inequalities by Graphing

Here, we will learn how to graph a second-degree inequality. When we graph a second-degree inequality, we use the following steps: Graph the boundary, replace the inequality symbol with an equality symbol. Graph the resulting equation. The boundary is solid for a non-strict inequality or dashed for a strict inequality. We can then use a test point to find and shade the solution region. Recall that the test point can be any point that is not on the boundary.
If the test point works in the original inequality, the test point lies in the solution region. If the test point fails in the original inequality, the test point lies in the non-solution region. When we encounter a system of non-linear inequalities, we will begin by graphing each inequality separately. Once this is done, we will shade the overlap between the graphs. This overlap is the section of the graph that satisfies all inequalities of the system.